2

I want to calculate the radius of curvature of a meandering river with ArcGIS 10.1. I have used the Planform Statistic Tool, developed by the National Center for Earth-surface Dynamics, to calculate width and radius of curvature (Rc), but according to the authors of the tool, the values of Rc show a significant local scatter in a first-order curvature estimate, and they recommended that higher order schemes be used or curvature be smoothed prior to additional analysis.
These are the results that I got:

enter image description here

Doing a moving average of the values will be enough for smoothing the curvature? If so, doing a 3-values moving average, for example, will be enough? these are the results:

enter image description here

How can I interpret those data? The program has calculated 991 values (for the whole line of the river). enter image description here

I'm calculating the Rc because I want to compare the radius of curvature with the width (Rc/w) to see the efficiency of the river, and with all these values I don't know how to do that.

So, there is another way to calculate the radius of curvature of the river? I have read the other post but I think that I can't use for this case.

PolyGeo
  • 65,136
  • 29
  • 109
  • 338
Krahsin
  • 105
  • 2
  • 10
  • Do you want to do this via an equation in Excel, or script a solution in ArcMap? What you're currently calculating is the radius of curvature at a particular point along the line, rather than along the extent of a whole curve -- this may be a more accurate approach since you're looking at a natural system with variation in curvature (I have only looked at curvature of roads, which are pretty constant) but your moving average is somewhat problematic at inflection points where the curve is changing direction (i.e, starts turning left instead of turning right or vice versa). – Erica Dec 19 '14 at 12:28
  • @Erica You are completely right. My moving average is not working at all. I want to calculate Rc via ArcMap, but I’m struggling with that, so I tried another solutions, that obviously, din't work. How can I calculate Rc with ArcMap? Do I need to pick up the start and end point of every single meander? and if so, How can I do that? – Krahsin Dec 19 '14 at 13:28
  • 1
    It isn't a simple solution; the best I've ever managed to accomplish is roughly described in this Answer, and involved a Python script that could find the point of inflection (e.g. start and end points of meanders) and then evaluated the change around the curve. It didn't account for variation in curvature (e.g. a gentle left-curve transitioning to a sharper left-curve), though. I mostly mention this to point out that unfortunately it isn't a simple problem; I don't have that Python script anymore :( – Erica Dec 19 '14 at 13:45
  • An additional note from that Answer, just to emphasize it -- my solution didn't use the true calculus approach that would most accurately measure the radius of curvature, it was still an approximation. The calculus presumably can be done in Python, but it wasn't something I had time to dig into when I was working on that project. – Erica Dec 19 '14 at 13:52

1 Answers1

3

It is a well-studied problem, to estimate curvature from a digitized curve. There is no simple answer. See this paper for a comparison of several algorithms:

Simon Hermann and Reinhard Klette. "A Comparative Study on 2D Curvature Estimators." CITR, The University of Auckland, New Zealand, 2006. (Author link).

          Fig7
Joseph O'Rourke
  • 321
  • 2
  • 5
  • Thanks. I've read your paper and others similar, but still looking for some solution to apply on arcmap – Krahsin Dec 20 '14 at 14:05